I think you're right with the first point you raised - the type of the survey will determine the way you display the results.
Showing the numbers is pretty important to distinguish the validity of the survey results. Obviously a small sample size is very likely to skew the results and in most cases this is not a good thing.
An issue with displaying the results in the case of a survey with a limited number of responses, is that if there's not a lot of responses, perhaps people will refrain from voting ('nobody uses this thing') or be inclined to ignore the results based on the low number of responses.
Someone has already raised this point above, where a company may want to appear bigger than they are, and showing a small number of votes won't help with this.
A common behaviour is to not show the results until after the poll, which negates the impact that the results have on the actual vote itself, which to me is one of the most important things - I think doing any poll you want to protect the validity of the results, regardless of how many people respond, and one way of doing this is hiding results until after the vote, numbers or no numbers displayed. (See Conformity on Wikipedia)
It seems to me that in most cases displaying the number of votes is going to be more helpful than not though. I've tried to have a look for some studies into this but it seems hard to find so I'm basing this on my own opinion and deducing from common logic - certainly open to interpretation but hope I've helped a little.